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<H3>fix neb command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID neb Kspring 
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>neb = style name of this fix command
<LI>Kspring = inter-replica spring constant (force/distance units) 
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 active neb 10.0 
</PRE>
<P><B>Description:</B>
</P>
<P>Add inter-replica forces to atoms in the group for a multi-replica
simulation run via the <A HREF = "neb.html">neb</A> command to perform a nudged
elastic band (NEB) calculation for transition state finding.  Hi-level
explanations of NEB are given with the <A HREF = "neb.html">neb</A> command and in
<A HREF = "Section_howto.html#howto_5">Section_howto 5</A> of the manual.  The fix
neb command must be used with the "neb" command to define how
inter-replica forces are computed.
</P>
<P>Only the N atoms in the fix group experience inter-replica forces.
Atoms in the two end-point replicas do not experience these forces,
but those in intermediate replicas do.  During the initial stage of
NEB, the 3N-length vector of interatomic forces Fi = -Grad(V) acting
on the atoms of each intermediate replica I is altered, as described
in the <A HREF = "#Henkelman1">(Henkelman1)</A> paper, to become:
</P>
<PRE>Fi = -Grad(V) + (Grad(V) dot That) That + Kspring (|Ri+i - Ri| - |Ri - Ri-1|) That 
</PRE>
<P>Ri are the atomic coordinates of replica I; Ri-1 and Ri+1 are the
coordinates of its neighbor replicas.  That (t with a hat over it) is
the unit "tangent" vector for replica I which is a function of Ri,
Ri-1, Ri+1, and the potential energy of the 3 replicas; it points
roughly in the direction of (Ri+i - Ri-1); see the
<A HREF = "#Henkelman1">(Henkelman1)</A> paper for details.
</P>
<P>The first two terms in the above equation are the component of the
interatomic forces perpendicular to the tangent vector.  The last term
is a spring force between replica I and its neighbors, parallel to the
tangent vector direction with the specified spring constant <I>Kspring</I>.
</P>
<P>The effect of the first two terms is to push the atoms of each replica
toward the minimum energy path (MEP) of conformational states that
transition over the energy barrier.  The MEP for an energy barrier is
defined as a sequence of 3N-dimensional states which cross the barrier
at its saddle point, each of which has a potential energy gradient
parallel to the MEP itself.
</P>
<P>The effect of the last term is to push each replica away from its two
neighbors in a direction along the MEP, so that the final set of
states are equidistant from each other.
</P>
<P>During the second stage of NEB, the forces on the N atoms in the
replica nearest the top of the energy barrier are altered so that it
climbs to the top of the barrier and finds the saddle point.  The
forces on atoms in this replica are described in the
<A HREF = "#Henkelman2">(Henkelman2)</A> paper, and become:
</P>
<PRE>Fi = -Grad(V) + 2 (Grad(V) dot That) That 
</PRE>
<P>The inter-replica forces for the other replicas are unchanged from the
first equation.
</P>
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>.  None of the <A HREF = "fix_modify.html">fix_modify</A> options
are relevant to this fix.  No global or per-atom quantities are stored
by this fix for access by various <A HREF = "Section_howto.html#howto_15">output
commands</A>.  No parameter of this fix can
be used with the <I>start/stop</I> keywords of the <A HREF = "run.html">run</A> command.
</P>
<P>The forces due to this fix are imposed during an energy minimization,
as invoked by the <A HREF = "minimize.html">minimize</A> command via the
<A HREF = "neb.html">neb</A> command.
</P>
<P><B>Restrictions:</B>
</P>
<P>This command can only be used if LAMMPS was built with the REPLICA
package.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A> section
for more info on packages.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "neb.html">neb</A>
</P>
<P><B>Default:</B> none
</P>
<A NAME = "Henkelman"></A>

<P><B>(Henkelman1)</B> Henkelman and Jonsson, J Chem Phys, 113, 9978-9985 (2000).
</P>
<A NAME = "Henkelman"></A>

<P><B>(Henkelman2)</B> Henkelman, Uberuaga, Jonsson, J Chem Phys, 113,
9901-9904 (2000).
</P>
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